Using Solar p-Modes to Determine the Convection Zone Depth and Constrain Diffusion-produced Composition Gradients

Low- and intermediate-degree solar p-mode frequencies, which are sensitive to the solar structure near the bottom of the convection zone, are used to find the convection zone depth and to constrain the size and shape of composition gradients produced by diffusive settling of helium and heavier elements. We have calculated the evolution and nonadiabatic oscillation frequencies of solar models incorporating the latest Mihalas, Dappen, Hummer, and Mihalas (MHD) equation of state, OPAL opacities, and diffusion of hydrogen, helium, and several heavier elements. Comparisons between observed and calculated p-mode frequencies indicate (1) the solar convection zone base is at 0.712 +/- 0.001 solar radii; (2) the solar convection zone helium mass fraction Y is very near 0.240 (+/- 0.005), or about 0.024 less than the initial abundance required to match the solar luminosity; (3) the diffusion-produced Y and Z composition gradients below the convection zone are fairly steep and not smoothed significantly by turbulence. This implies that turbulent mixing below the convection zone cannot cause most of the solar lithium destruction during the main sequence.